Category:Meta-GGA: Difference between revisions
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== Theoretical Background == | == Theoretical Background == | ||
Meta-GGA exchange-correlation functionals depend on the electron density <math>\rho</math>, its first derivative <math>\nabla\rho</math> and | Meta-GGA exchange-correlation functionals depend on the electron density <math>\rho</math>, its first derivative <math>\nabla\rho</math> and the kinetic-energy density <math>\tau</math>: | ||
:<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(\rho,\nabla\rho,\tau)d^{3}r</math> | :<math>E_{\mathrm{xc}}^{\mathrm{meta-GGA}}=\int\epsilon_{\mathrm{xc}}^{\mathrm{meta-GGA}}(\rho,\nabla\rho,\tau)d^{3}r</math> | ||
Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropraie for very large systems. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the electronic band structure like the band gap. The meta-GGA that is currently widely used in solid-state physics is SCAN{{cite|sun:prl:15|}}. | Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropraie for very large systems. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the electronic band structure like the band gap. The meta-GGA that is currently widely used in solid-state physics is SCAN{{cite|sun:prl:15|}}. | ||
Revision as of 10:41, 19 January 2022
Theoretical Background
Meta-GGA exchange-correlation functionals depend on the electron density , its first derivative and the kinetic-energy density :
Although meta-GGAs are slightly more expensive than GGAs, they are still fast to evaluate and appropraie for very large systems. They are very often sufficiently accurate for the geometry optimization or the cohesive energy, but less recommended for properties related to the electronic band structure like the band gap. The meta-GGA that is currently widely used in solid-state physics is SCAN[1].